Epsilon-tube filter for blunt noise removal

ABSTRACT

The present application describes techniques to filter signals contaminated with blunt noise. Calculated filter coefficients may be applied to signals to generate filtered output signals without the blunt noise. Sets of filter coefficients may be calculated utilizing an ε-tube filter process in conjunction with an autoregressive exogenous (ARX) model. Sets of filter coefficients may be calculated in accordance with a constrained optimization algorithm using data indicative of a source of the blunt noise. When the blunt noise is modeled in accordance with the ARX model, filtered output signals are generated having amplitudes constrained to a selected Epsilon value, which may be the amplitude of a primary component of the unfiltered signal. A set of filter coefficients may be calculated by determining, from the set of filter coefficients that satisfy the constrained optimization algorithm, a solution that produces a filtered output signal having the most time-invariant frequency composition.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the priority benefit under 35 U.S.C. §119(e) ofU.S. Provisional Patent Application No. 61/912,616, filed Dec. 6, 2013,the disclosure of which is incorporated herein by reference in itsentirety.

STATEMENT OF GOVERNMENTAL INTEREST

This invention was made with government support under W81XWH-09-C-0117,awarded by the U.S. Army/MRMC. The Government has certain rights in theinvention.

FIELD OF INVENTION

The present disclosure generally relates to systems, methods, apparatus,and non-transitory media for filtering signals and, more particularly,to filtering signals by removing blunt noise that is mixed with thesignals.

BACKGROUND

For patients suffering from a variety of injuries or disease states suchvenous thrombosis, burns, trauma, various types of heart conditions,sepsis, various types of encephalopathy, dehydration, renal failure,dialysis, hypertension, neuromuscular diseases, low-back pain, motorcontrol disorders, etc., signals generated via relevant medicaldiagnostic equipment may provide valuable insight for medicalprofessionals.

However, in many medical diagnostic examinations, a diagnostic signalgenerated by the relevant diagnostic equipment may include noise and/orartifacts. Noise and/or artifacts may be introduced into the diagnosticsignal due to a presence of one or more extraneous factors that mayinfluence the diagnostic signal while the test is being performed, suchas the patient's movement during the test, electrical noise, etc.Because the noise may have an amplitude larger than the diagnosticsignal itself and/or be dynamic or non-repetitive in nature,conventional signal filtering methods may attenuate or distort thediagnostic signal. In addition, conventional attempts to removeartifacts from diagnostic signals using multi-channel recordings of thediagnostic signal may add unwanted complexity, size, and cost to thediagnostic equipment.

As a result, performing signal filtering with portable diagnosticequipment to remove artifacts while recovering the signal of interestpresents several challenges.

SUMMARY

The present application describes techniques to filter signals havingmixed blunt noise, which may be characterized as noise having relativelyhigh amplitudes and low frequencies having a frequency spectrum thatoverlaps with that of the signal of interest. Filtering may beaccomplished using a two-step process to implement an Epsilon-tube(ε-tube) filter.

First, an autoregressive exogenous (ARX) model may be used to generateblunt noise models using sets of filter coefficients applied to dataassociated with the source of the blunt noise. When the ARX models aresubtracted from the original signal using sets of filteringcoefficients, the filter provides a set of potential filtered outputsignals having corresponding filter coefficient solutions that satisfy aconstrained optimization algorithm. This optimization algorithm ensuresthat the filter coefficient solutions result in filtered signals havinga maximum amplitude (the ε-tube) equal to (or nearly equal to) that ofthe diagnostic signal.

Second, a filter coefficient solution may be selected from the solutionssatisfying the constrained optimization algorithm by selecting thefiltered output signal having most “regular” solution. Signal regularitymay be determined by analyzing the filtered output signals in thefrequency domain to determine the filter coefficient solution that hasthe most time-invariant frequency composition. In one example, aStockwell-transform algorithm may be utilized to implement thisdetermination. In this way, the two-step ε-tube filtering process avoidsissues associated with conventional filtering methods, such as modelingthe diagnostic signal of interest as well as the artifacts and/or theintroduction of distortion into the filtered output signal.

In an example, a method includes one or more processors applying aselected set of filter coefficients having a frequency composition thatis the least frequency-varying of the plurality of filtered signals thatsatisfy an Epsilon constraint.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

The figures described below depict various aspects of the system andmethods disclosed herein. It should be understood that each figuredepicts an aspect of a particular aspect of the disclosed system andmethods, and that each of the figures is intended to accord with apossible aspect thereof. Further, wherever possible, the followingdescription refers to the reference numerals included in the followingfigures, in which features depicted in multiple figures are designatedwith consistent reference numerals.

FIG. 1 illustrates a block diagram of an exemplary system 100 inaccordance with an exemplary aspect of the present disclosure;

FIG. 2A illustrates a graphical representation of an IP signalcontaminated with blunt noise;

FIG. 2B illustrates a graphical representation of a accelerometersignals corresponding to the source of the blunt noise shown in FIG. 2A;

FIG. 3A illustrates a graphical representation of an IP signalcontaminated with blunt noise and a reference CO₂ signal;

FIG. 3B illustrates a graphical representation of a filtered IP signalafter ε-tube filtering;

FIG. 3C illustrates a graphical representation of a filtered IP signalafter application of ε-tube filtering as shown in FIG. 2B andapplication of regularization;

FIG. 4A illustrates a graphical representation of a Stockwell-transformof a filtered IP signal using a set of filter coefficients that satisfythe minimized constraint of Eqn. 2 but without regularization;

FIG. 4B illustrates a graphical representation of a Stockwell-transformof a filtered IP signal using a set of filter coefficients that satisfyboth the minimized constraint of Eqn. 2 after the application ofregularization; and

FIG. 5 illustrates an example method 500 in accordance with an exemplaryaspect of the present disclosure.

DETAILED DESCRIPTION

The present application describes various embodiments in the context oftechniques using diagnostic systems to generate, measure, receive,sample, analyze, process, and/or filter one or more diagnostic signals.These diagnostic systems may include those used to non-invasively orinvasively monitor one or more biological processes for a patientundergoing a test procedure. For example, diagnostic systems may be usedmonitor changes in the volume of blood in the venous system of patients.Such techniques may utilize an impedance plethysmography system as oneexample, but may also include any suitable type of diagnostic systemsuch as photoplethysmography, electromyography, ultrasound, etc.

Furthermore, the embodiments described herein are applicable to anysuitable type of system having periodic signals that may be prone tonoise contamination. In various embodiments, this may include medical ornon-medical diagnostic systems. For example, the filtering methodsdescribed herein may be applied to medical diagnostic systems configuredto generate, measure, receive, sample, analyze, process, and/or filtersignals associated with electrocardiograms, impedance cardiography,arterial blood pressure waveforms, venous blood pressure waveforms,intracranial pressure waveforms, photoplethysmography waveforms,end-tidal carbon dioxide waveforms, Doppler signals, piezoelectricsignals, etc.

To provide additional examples, the filtering methods described hereinmay also be applied to non-medical diagnostic systems configured togenerate, measure, receive, sample, analyze, process, and/or filtersignals associated with exercise equipment, biometric sensors, fitnesstrackers, wearable electronic devices, etc.

Impedance Plethysmography and Respiratory Rate

The various embodiments explained herein often refer to impedanceplethysmograph (IP) signals as illustrative examples, but theseembodiments are equally applicable to any suitable type of electricalsignal that may be adequately sampled and filtered in accordance withthe techniques presented herein. A brief explanation of impedanceplethysmographs is presented below for clarity.

Conventionally, impedance plethysmographs (IPs) may be used to determinechanges in blood volume within portions of a patient's limb, which isparticularly useful in diagnosing conditions such as venous thrombosis.Impedance plethysmographs typically function by injecting ahigh-frequency, low amplitude sinusoidal current into a segment ofinterest using a pair of skin electrodes, or current electrodes. Anotherpair of electrodes is also used to measure an imposed voltage differencebetween the current injection points, which is caused by the passage ofelectrical current through the patient's tissue. A diagnostic signal, inthis case an IP signal, may then be generated based upon a ratio betweenthe measured voltage and the injected current. Because the electricalconductivity of the tissue is mainly influenced by the volume of bloodin that region, variations of the measured voltage (and thus variationsin the impedance) cause the IP signal to reflect variations caused bythe blood's electrical conductivity in the segment of interest due tochanges in blood volume.

One of the main sources of blood volume variation and tissue movement,in particular in the chest and abdomen area, is respiration. As aresult, the respiratory signal and the respiratory rate may be extractedfrom an IP signal acquired from the thorax and abdomen area when thesubject is motionless. However, a patient's movement is also a largesource of blood volume variation. As a result, a patient's movementduring an administered IP test may result in drastic variations in themeasured IP signal resulting in blunt noise, in this case “motionartifacts” (MA) having amplitudes larger than the amplitude of therespiratory component of the IP signal. As a result, it is desirable touse filtering methods to eliminate the MA's before the signal is usedfor monitoring respiration.

FIG. 1 illustrates a block diagram of an exemplary system 100 inaccordance with an exemplary aspect of the present disclosure. System100 may include a data acquisition system 102, a diagnostic dataacquisition unit 150, n number of electrodes 152.1-152.n, and a modelingdata acquisition unit 170.

Diagnostic data acquisition unit 150 may be implemented as any suitabletype of diagnostic device configured to receive signals via electrodes152.1-152.n. Depending on the particular type of test that is performed,diagnostic data acquisition unit 150 may be implemented as one or moretypes of diagnostic devices. Diagnostic data acquisition unit 150 may beconfigured to receive signals via electrodes 152.1-152.n, to processthese signals, and/or to send the signals received via electrodes152.1-152.n and/or the processed signals to data acquisition system 102.In one example, diagnostic data acquisition unit 150 may be part of aBiopac system, such as the Biopac EBI100C electrobioimpedance amplifier,manufactured by Biopac Systems, Inc. of Aero Camino Goleta, Calif.

Electrodes 152.1-152.n may be configured as any suitable type of deviceto measure, monitor, and/or generate electrical signals based upon theirlocation on a test subject and/or the type of test being performed viadiagnostic data acquisition unit 150. For example, if diagnostic dataacquisition unit 150 is implemented as the EBI100C electrobioimpedanceamplifier, then electrodes 152.1-152.n may be configured in accordancewith a system that is compatible with such a system. To provide anotherexample, if diagnostic data acquisition unit 150 is used to conduct anIP test, some of electrodes 152.1-152.n may be configured as currentinjecting electrodes while some of electrodes 152.1-152.n may beconfigured as voltage monitoring electrodes. Thus, electrodes152.1-152.n may provide diagnostic data acquisition unit 150 with theappropriate signals to generate one or more IP signals and/or to sendthe IP signals to data acquisition system 102.

Electrodes 152.1-152.n may be placed in any suitable location to providesignals in accordance with the type of application and/or the test beingconducted. For example, if an electrocardiography (ECG) measurement isperformed, one or more of electrodes 152.1-152.n may be placed on asuitable portion of a patient's chest. To provide another example, if anIP test is performed, one or more of electrodes 152.1-152.n may beplaced on a suitable portion of the patient commensurate with an IPtest, such as between the patient's third and tenth ribs, a traditionaltrans-thoracic electrode placement, etc.

Modeling data acquisition unit 170 may be configured to measure,generate, receive, and/or monitor one or more data signals associatedwith the source of noise introduced into the diagnostic signal measuredby diagnostic data acquisition unit 150. Modeling data acquisition unit170 may be implemented as any number and/or type of sensors based uponthe source of the noise introduced into the diagnostic signal that is tobe modeled.

In an embodiment, the noise may include, for example, blunt noise. Inembodiments in which the blunt noise takes the form of MAs, modelingdata acquisition unit 170 may be implemented as one or more sensorsconfigured to monitor the patient's movement. Some examples of thesetypes of sensors may include accelerometers, pressure sensors,piezoelectric sensors, etc. To provide an illustrative example, modelingdata acquisition unit 170 may be implemented as a three-axisaccelerometer configured to measure acceleration in the x, y, andz-axes. Modeling data acquisition unit 170 may be worn by and/orattached to a patient such that these accelerometer signals representone or more movement parameter values indicative of the patient'smovement in each of the x, y, and z-axes. Modeling data acquisition unit170 may be configured to transmit the acceleration signals and/or one ormore movement parameter values to data acquisition system 102.

Data acquisition system 102 may include a central processing unit (CPU)104, a graphics processing unit (GPU) 106, a display 108, acommunication unit 110, a user interface 112, and a memory 114. Invarious embodiments, data acquisition system 102 may be implemented asany suitable computing device, such as a smartphone, a mobile device, atablet computer, a laptop computer, a dedicated diagnostic system, apersonal computer, a wearable computing device, etc.

In some embodiments, data acquisition system 102 may be implemented as asingle device, for example, as shown in FIG. 1. Such implementations maybe particularly useful when a portable and/or mobile device isdesirable. In other embodiments, data acquisition system 102 may beimplemented as a device that may perform functions of two or moredevices, such as a device that may perform functions of both dataacquisition system 102 and diagnostic data acquisition unit 150, forexample. Such implementations may be particularly useful when it isdesirable to modify an existing off-the-shelf system to perform theembodiments as described herein, for example, by performing a softwareand/or firmware upgrade, by adding specialized hardware cards ormodules, etc.

Display 108 may be implemented as any suitable type of display and mayfacilitate user interaction in conjunction with user interface 112, suchas a mobile device display, a smartphone display, a capacitive touchscreen display, a resistive touch screen display, etc. In variousaspects, display 108 may be configured to work in conjunction with CPU104 and/or GPU 106 to display one or more diagnostic signals receivedand processed by communication unit 110 and/or filtered by CPU 104executing instructions in one or more modules stored in memory 114.

Communication unit 110 may be configured to process, send signals to,and/or receive signals from diagnostic data acquisition unit 150 and/ormodeling data acquisition unit 170. Communication unit 110 may beconfigured to communicate with diagnostic data acquisition unit 150and/or modeling data acquisition unit 170 in accordance with anysuitable type and/or number of wired and/or wireless communicationprotocols.

User interface 112 may be configured to receive user-input and tofacilitate user interaction with data acquisition system 102. Forexample, user-interface 112 may be implemented as a “soft” keyboard thatis displayed on display 108, an external hardware keyboard communicatingvia a wired or a wireless connection (e.g., a Bluetooth keyboard), anexternal mouse, or any other suitable user-input device.

User-interface 112 may include a microphone configured to receive userinput in the form of voice input, such as voice commands, for example.In some aspects, voice commands received via user interface 112 may beconverted to text, for example, via CPU 104. In this way, user interfacedevice 112 may allow a user to enter text in lieu of typing. Userinterface 112 may facilitate a user adjusting, modifying, changing,etc., one or more options or settings of data acquisition system 102depending on a particular implementation. For example, a user mayutilize user interface 112 to change display settings, to change one ormore design parameters used in the signal filtering process as furtherdiscussed below, etc.

CPU 104 and/or GPU 106 may be configured to communicate with memory 114to store to and read data from memory 114. In accordance with variousembodiments, memory 114 is a computer-readable non-transitory storagedevice that may include any combination of volatile (e.g., a randomaccess memory (RAM), or a non-volatile memory (e.g., battery-backed RAM,FLASH, etc.). Memory 114 may be configured to store instructionsexecutable on CPU 104 and/or GPU 106. These instructions may includemachine-readable instructions that, when executed by CPU 102 and/or GPU106, cause CPU 102 and/or GPU 106 to perform various acts.

Data acquisition module 115, modeling module 117, regularization module119, and filtering module 121 are portions of memory 114 configured tostore instructions executable by CPU 104 and/or GPU 106. In accordancewith various embodiments, any of data acquisition module 115, modelingmodule 117, regularization module 119, and/or filtering module 121 mayoperate as a separately executable software application, a plugin thatextends the functionality of another software application such as a webbrowser, an application programming interface (API) invokable by asoftware application, etc. The instructions included within any of anyof data acquisition module 115, modeling module 117, regularizationmodule 119, and/or filtering module 121 may be compiled and executableon CPU 104 and/or GPU 106 directly, or not compiled and interpreted bythe CPU 104 and/or GPU 106 on a runtime basis.

Data acquisition module 115 may include instructions that, when executedby CPU 104 and/or GPU 106, causes CPU 104 and/or GPU 106 to receive,store, and/or process data received from diagnostic data acquisitionunit 150 and/or modeling data acquisition unit 170 via communicationunit 110. In various embodiments, this data may include, for example,sampled data representative of signals received from diagnostic dataacquisition unit 150 over one or more processing windows, datarepresentative of signals received from modeling data acquisition unit170 over one or more processing windows, etc.

Modeling module 117 may include instructions that, when executed by CPU104 and/or GPU 106, causes CPU 104 and/or GPU 106 to retrieve datastored by data acquisition module 115 and to utilize this data toconstruct one or more models of blunt noise that may be mixed with thesignals received by diagnostic data acquisition unit 150 over one ormore processing windows. The instructions stored in modeling module 117may facilitate CPU 104 and/or GPU 106 to construct blunt noise modelsusing any suitable type of modeling process or algorithm, such astangent sigmoid activation functions, autoregressive exogenous models,etc.

In various embodiments, modeling module 117 may include instructions tofacilitate the modeling of blunt noise using the sampled data measuredby modeling data acquisition unit 170, which may be indicative of thesource of the blunt noise. In embodiments in which the blunt noise iscaused by a patient's movement, modeling module 117 may includeinstructions to construct models using one or more movement parametervalues, which may include one or more accelerometer signal values. Thetechniques represented by the instructions to construct models arefurther discussed in detail below.

As will be discussed below in further detail, one or more blunt noisemodels may be constructed based upon sets of filter coefficients thatmay be applied to the sampled data measured by modeling data acquisitionunit 170 to attempt to estimate the blunt noise. To filter the signalcontaminated with blunt noise, the original contaminated signal may befiltered according to one or more sets of filter coefficients such thatthe blunt noise model is subtracted from the original signal to producea filtered signal. To avoid distortion of the filtered signal, an ε-tubevalue is used to constrain the calculated filter coefficients to thosesolutions that provide filtered signal amplitudes having amplitudes lessthan the amplitude of the primary component of the original contaminatedsignal.

In this way, modeling module 117 includes instructions to facilitate thecalculation of sets of filter coefficient solutions by CPU 104 and/orGPU 106 that produce filtered signals having amplitudes that are“clamped” by the ε-tube. Because several sets of filter coefficients maysatisfy this constraint, additional calculations, which are furtherdiscussed below, may be used to further narrow the filter coefficientsolution.

In some embodiments, modeling module 117 may include instructions to setone or more values, such as the Epsilon value and/or other modelingparameters to be further discussed below, based upon characteristics ofthe measured signal such as amplitude, frequency, etc. In otherembodiments, modeling module 117 may include instructions to allow auser to specify these values, for example, via user interface 112

Regularization module 119 may include instructions that, when executedby CPU 104 and/or GPU 106, causes CPU 104 and/or GPU 106 to select oneof the sets of filter coefficients, from those that satisfy the ε-tubeconstraint, which yields a filtered signal having a frequencycomposition that is the least frequency-varying of the solutions. Theinstructions stored in regularization module 119 may facilitate CPU 104and/or GPU 106 to select a filtering solution using any suitable type offrequency transform and/or algorithm, such as a Stockwell-Transform, forexample, as further discussed below.

Filtering module 121 may include instructions that, when executed by CPU104 and/or GPU 106, causes CPU 104 and/or GPU 106 to store and/orprocess data used in conjunction with the overall filtering processimplemented by data acquisition system 102 in accordance with theembodiments as described herein. For example, filtering module 121 maystore, as part of its instructions, data such as defined filter designvariables, sliding time window scales, processing windows and/or slidingwindows, design constraints, one or more filter parameters, definedslack variables, user selections, filter coefficients, ε-tube values,and/or predetermined constants used by data acquisition system 102 tofilter diagnostic signals. To provide another example, filtering module121 may include instructions that, when executed by CPU 104 and/or GPU106, causes CPU 104 and/or GPU 106 to apply the filter coefficientsolutions to the diagnostic signals, to perform diagnostic signalfiltering in real-time and/or as part of one or more batch processesafter the diagnostic signal has been sampled and stored in memory 114.

In some embodiments, filtering module 121 may include instructions thatcause CPU 104 and/or GPU 106 to work in conjunction with user interface112, for example, to receive data used in conjunction with the overallfiltering process. In this way, a user may originally program theinstructions stored in filtering module 121, for example, and lateroverwrite these instructions to update the data.

In other embodiments, filtering module 121 may include instructions thatcause CPU 104 and/or GPU 106 to work in conjunction with communicationunit 110, for example, to set one or more data values used in thefiltering process, such as the Epsilon value and/or other modelingparameters to be further discussed below, based upon characteristics ofthe measured signal such as amplitude, frequency, etc.

FIG. 2A illustrates a graphical representation of an IP signalcontaminated with blunt noise. In an embodiment, IP signal 202 may bemeasured via one or more of electrodes 152.1-152.n and sampled and/orprocessed by diagnostic data acquisition unit 150. Again, IP signal 202,or data samples representative thereof, may be received by dataacquisition system 102 via, for example, communication unit 110.

The embodiments described herein may be applicable to filter anysuitable type of periodic signal, but IP signal 202 is shown in FIG. 2Afor illustrative purposes. In addition to IP signal 202, FIG. 2A alsoincludes a CO₂ signal 206 for comparative purposes. Because IP signalsmeasure changes in blood volume over a measure portion of a patient'sbody, a large contributor to these volumetric changes is the patient'sbreathing. Another contributing factor to blood volume changes is thepatient's heart rate, which can also be observed as the high frequencyripple present throughout IP signal 202. CO₂ signal 206 is not neededfor the filtering process, but shows how IP signal 202 tracks thepatient's breathing rate. The primary portion of IP signal 202 thattracks the patient's respiratory rate, therefore, is often referred toas the respiratory component of IP signal 202.

IP signal 202 also includes blunt noise 204. In this example, bluntnoise 204 may be associated with a motion artifact caused by thepatient's movement, resulting in a sudden change in blood volume. Asshown in FIG. 2A, blunt noise 204 has an amplitude greater than therespiratory component of IP signal 202 and a relatively low frequency.

FIG. 2B illustrates a graphical representation of accelerometer signalscorresponding to the source of the blunt noise shown in FIG. 2A.Assuming that blunt noise 204 corresponds to a MA, the accelerometersignals for each of the x, y, and z axes as shown in FIG. 2B mayindicate the source of the MA, which is indicated by the correlation intime between blunt noise 204 and the variations in the accelerometervalues in FIGS. 2A and 2B. In an embodiment, the accelerometer signalsshown in FIG. 2B may be measured, sampled, and/or processed by modelingdata acquisition unit 170 via one or more of appropriate accelerometersensors attached to the patient while the IP test is being performed.The accelerometer signals shown in FIG. 2B, or data samplesrepresentative thereof, may also be received by data acquisition system102 via, for example, communication unit 110. In an embodiment, the datasample values for each of the accelerometer signals at each samplingpoint within a processing window may be stored as movement parametervalues in a suitable portion of memory 114. As will be further explainedbelow in mathematical terms, these movement parameter values may berepresented as vector representations to determine an appropriate set offilter coefficient solutions that, when used to filter the contaminatedIP signal 202, may remove MA 204 from IP signal 202.

ε-Tube and Autoregressive Exogenous Models

The ε-tube filter process refers to filtering using a defined errorterm, ε, which ensures the filtered signal is constrained within a“tube,” or amplitude, set by ε. CPU 104 and/or GPU 106 may executeinstructions stored in modeling module 117 to calculate one or more setsof filter coefficients, which may be applied to an input signal via CPU104 and/or GPU 106 may executing instructions stored in filtering module121 to provide a filtered output signal such that the amplitude of theoutput does not violate the tube constraint.

The set of filter coefficients may be calculated to model the bluntnoise but not the primary component of the signal using, for example,data measured via modeling data acquisition unit 170. When this modeledsignal is subtracted from the original signal that is contaminated withthe blunt noise, the difference between the filtered signal and theoriginal diagnostic signal is constrained by the ε-tube value. Bysetting the ε-tube values to the amplitude of the primary component ofthe original diagnostic signal, ε-tube filtering advantageously preventsestimation errors from affecting regions of the diagnostic signalneighboring the blunt noise. In other words, setting appropriate ε-tubevalues prevents the calculation of filter coefficients that would resultin the primary component of the signal being filtered when the filteringcoefficients are applied to the input signal.

The concept of ε-tube may be presented in the form of Vapnik's lossfunction, which allows for a margin, called the tube, in which the errorthat is assigned to the points that fall inside the tube is zero. Inmathematical terms, Vapnik's loss function may be represented as Eqn. 1below:

|g _(t) −y _(t)(U,w)|_(ε)=max(0,|g _(t) −y _(t)(U,w)|−ε)  (1)

Using system 100 as an example, g_(t) may represent the value of asignal at time t. This signal may include, for example, the diagnosticsignal measured by diagnostic data acquisition unit 150 via one or moreelectrodes 152.1-152.n. Again, in an embodiment, this diagnostic signalmay correspond to an IP signal. Further using system 100 as an example,y_(t) may represent the output of a filter at a time t implemented bydata acquisition system 100 using a calculated set of filtercoefficients, U may represent a matrix whose rows are the movementparameter values (e.g., accelerometer signals), w may represent thevector representing the calculated set of filter coefficients, and ε mayrepresent the width of the tube.

In other words, according to Eqn. 1, for points in which the differencebetween the filtered signal output and the input signal is less than ε(points that fall within the tube) there is a zero error. Furthermore,ε-tube filtering is well-suited to removing blunt noise from a signalthat is periodic in nature. This is particularly true given that theamplitude of the primary component of the input signal does not changerapidly over a relatively short period of time (e.g., 1 second) andtypically has a regular recurring pattern (e.g., a respiratorycomponent). That is, the main component of an IP signal is respiration,which is periodic and has nearly-constant amplitude within short periodsof time. As a result, the ε-tube may be used to estimate the blunt noisewhile avoiding filter coefficients from being calculated that also modelthis respiratory component by forming a tube around the IP signal thatonly encompasses the respiratory component.

In an embodiment, filter module 121 may include instructions, that whenexecuted by CPU 104 and/or GPU 106, causes CPU 104 and/or GPU 106 toimplement an ε-tube filter that is formulated as a constrainedoptimization problem which can be expressed as Eqn. 2 below:

Minimize Σ_(t=0) ^(N−1)ζ_(t)+Σ_(t=0) ^(N−1)ζ′_(t)  (2)

subject to Eqns. 3-5 below:

g _(t) −t _(t)(U,w)≦ε+ζ_(t) ,t=0, . . . ,N−1,  (3)

y _(t)(U,w)−g _(t)≦ε+ζ′_(t) ,t=0, . . . ,N−1,  (4)

ζ_(t)≧0,ζ_(t)′≧0,t=0, . . . ,N−1,  (5)

where ζ_(t) and ζ_(t)′ are slack variables that are ideally zero whenthe filtered signal fits within the tube and grow linearly otherwise,and N is the length of the diagnostic signal over which the filtering isperformed, such as a the length of a processing window, for example.

Although data acquisition system 102 may utilize any type of blunt noisemodeling process, for example, by CPU 104 and/or GPU 106 executinginstructions stored in modeling module 117, an autoregressive exogenous(ARX) model may be preferable due to its flexibility in modeling theblunt noise. An ARX model may be represented by executable instructionsstored in modeling module 117 that facilitate the modeling of bluntnoise having generic shapes. In an embodiment, the ARX model may berepresented as Eqn. 6 below:

y _(t)=−Σ_(i=1) ^(n) ^(a) a _(i) y _(t−1)+Σ_(i=1) ^(n) ^(b) b _(i) ^(T)u _(t−i+1),  (6)

In Eqn. 6, n_(a), may represent the number of filter poles, while n_(b),may represent the number of filter zeros plus 1. The number of filterpoles and zeroes that are included as part of the executableinstructions stored in modeling module 117 may be considered designparameters of the overall filtering process. Thus, these may be variedbased upon the particular implementation of system 100, the type ofsignal that is measured, the sampling rate of the diagnostic signal, thedesired error margin of the filtered signal, processing speed, resourcelimitations, etc.

Further referring back to Eqn. 6 and using the example system 100 asshown in FIG. 1, a_(i) may represent an i-th feedback coefficient, u_(t)may represent a vector of movement parameter values (e.g., accelerometerdata) at a time t (i.e., a column of U associated with a sample time t)while b_(i) may represent the corresponding vector of the i-thfeedforward coefficients. Therefore, referring back to Eqn. 1, thevector w may be composed of a_(i)'s and the elements of b_(i)'s.Modeling module 117 may include instructions, therefore, that whenexecuted by CPU 104 and/or GPU 106, cause CPU 104 and/or GPU 106 tocalculate the vector w that minimizes Eqn. 2 subject to Eqns. 3-5.

However, due to mathematical representation of the ε-tube, the solutionfor w is unique only when the diagnostic signal is exactly periodic, hasa constant amplitude and a regular pattern, and the blunt noise includedin the signal is generated through an ARX modeling process. Becausethese assumptions are unlikely to be true when measuring an actualsignal, the calculated solution for w may not be unique, but insteadincludes a set of filter coefficients that satisfy the minimizedconstraint of Eqn. 2. This set of filter coefficients also includesthose filter coefficients by which the blunt noise has been generated.

FIG. 3A illustrates a graphical representation of an IP signalcontaminated with blunt noise and a reference CO₂ signal. Again, theembodiments described herein may be applicable to filter any suitabletype of periodic diagnostic signal, but an IP signal is shown in FIG. 3Afor illustrative purposes. Similar to FIG. 2A, FIG. 3A also shows a CO₂signal in addition to the IP signal for comparative purposes, but theCO₂ signal is not needed for the filtering process.

FIG. 3B illustrates a graphical representation of a filtered IP signalafter ε-tube filtering. FIG. 3B is an example of the IP signal shown inFIG. 3A being filtered via the application of a set of filtercoefficients that satisfy the minimized constraint of Eqn. 2. In otherwords, the filtered signal as shown in FIG. 3B has an error of zero(i.e., the filtered IP signal output is completely constrained withinthe ε-tube) and thus the calculated set of filter coefficients representone set of filter coefficients that satisfy an optimal solution to theminimized constraint of Eqn. 2.

However, the filtered IP signal does not resemble the shape of therespiratory component of the IP signal shown in FIG. 3A, as thecalculated set of filter coefficients shown in FIG. 3B yield a filteredoutput signal containing high frequency noise 302. As a result,embodiments include calculating a set of filter coefficients based upona second criterion to yield a filter coefficient solution that is mostlikely to be the generator of the blunt noise. Assuming that the signalfollows a regular pattern, such as the pattern corresponding to thepatient's respiration, for example, embodiments include utilizing theregularity of the signal as a second objective to maximize. This isshown mathematically in Eqn. 7 below:

Minimize f=Σ _(t=0) ^(N−1)ζ_(t)+Σ_(t=0) ^(N−1)ζ_(t) ′−cR(g,U,w),  (7)

Where g is the vector of contaminated signal values within theprocessing window, e.g., the IP signal. That is, Eqn. 7 may beimplemented as part of the instructions stored in regularization module119, as shown in FIG. 1. Thus, when executed by CPU 104 and/or GPU 106,instructions stored in regularization module 119 may cause CPU 104and/or GPU 106 to calculate a set of filter coefficients by selecting,from set of filter coefficients satisfying the minimized constraint ofEqn. 2, the filter coefficients that also satisfy Eqn. 7.

FIG. 3C illustrates a graphical representation of a filtered IP signalafter application of ε-tube filtering as shown in FIG. 2B andapplication of regularization. Additional details of how theinstructions stored in regularization module 119 may implement thisfunctionality are further discussed below.

Referring back to Eqn. 7, R(g, U, w) may represent a regularizationterm, which is discussed further below, while c may represent a designparameter that provides adjustment for a balance between the twoobjectives. Similar to the number of filter poles and zeroes, the designparameter c may be varied based upon the particular implementation ofsystem 100, processing speed, resource limitations, etc. A suitablevalue of c depends on the amplitude of the signals, which are in turnbased upon the particular test that is being performed. In experimentaltests using IP signals having amplitudes on the order of magnitude asthose discussed herein, suitable values for c may be 10 or 20, forexample. CPU 104 and/or GPU 106 may calculate a set of filtercoefficients corresponding to a filtered output signal having the mostregular pattern among the filter coefficients solutions that provide thesmallest error.

As used herein, a “regular signal” has a frequency composition that isinvariant as time progresses. In an embodiment, this property may bedetermined through the use of a Stockwell transform (S-transform). TheS-transform is a generalization of a short time Fourier transform andprovides a time-frequency representation of the signal that is sensitiveto irregularities in the signal. A discrete time S-Transform may berepresented mathematically by Eqns. 8-9 below:

$\begin{matrix}{{{{S_{y}\left\lbrack {{pT},\frac{n}{NT}} \right\rbrack} = {\sum\limits_{m = 0}^{N - 1}\; {{Y\left\lbrack \frac{m + n}{NT} \right\rbrack}^{- \frac{2\pi^{2}m^{2}}{n^{2}}}^{\frac{j\; 2\; \pi \; m\; p}{N}}}}},{n \neq 0}}{and}} & (8) \\{{{S_{y}\left\lbrack {{pT},\frac{n}{NT}} \right\rbrack} = {\frac{1}{N}{\sum\limits_{m = 0}^{N - 1}\; \left\lbrack \frac{m}{NT} \right\rbrack}}},{n = 0}} & (9)\end{matrix}$

In the above example, Y represents the Fourier transform of y, while p,and n represent the time and frequency indices of the S-transform,respectively. In addition, N represents the number of samples in thesignal while T represents the processing window. Furthermore, theinverse S-transform of S_(y) is defined mathematically by Eqn. 10 below:

$\begin{matrix}{{y\lbrack{kT}\rbrack} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}\; {\sum\limits_{p = 0}^{N - 1}\; {{S_{y}\left\lbrack {{pT},\frac{n}{NT}} \right\rbrack}^{\frac{j\; 2\; \pi \; {nk}}{N}}}}}}} & (10)\end{matrix}$

FIG. 4A illustrates a graphical representation of a Stockwell-transformof a filtered IP signal using a set of filter coefficients that satisfythe minimized constraint of Eqn. 2 but without regularization. Thiscould include, for example, a signal such as the filtered IP signalshown in FIG. 3B. The S-Transform of an ideal signal with a regularpattern would result in any two given points on the time axis havingidentical frequency decompositions. Therefore, an average correlationbetween different vertical “slices” of the S-transform may be used as ameasure for the regularity of the signal.

In other words, regularization module 119 may include instructions thatallow CPU 104 and/or GPU 106 to perform an S-Transform on one or more ofthe resulting filtered diagnostic signals, and to analyze the averagecorrelation of frequency compositions at different times within theprocessing window of the filtered signal. CPU 104 and/or GPU 106 maythen select the filter coefficients from those that produced filteredoutput signals satisfying the minimized constraint of Eqn. 2 and thatalso produce the most regular (i.e., least time-varying) filtered signalbased upon the S-Transform regularity analysis.

In one embodiment, the regularization analysis may be performed throughthe use of the S-Transform, because S-transforms provide a particularadvantage given their sensitivity to signal irregularities. However, inother embodiments, alternative regularization techniques may beimplemented, such as an analysis of one or more features extracted froma Fourier transform of the signal, an analysis of signal variance,kurtosis, entropy, an analysis of one or more features extracted from aWavelet transformation of the signal, etc.

FIG. 4B illustrates a graphical representation of a Stockwell-transformof a filtered IP signal using a set of filter coefficients that satisfyboth the minimized constraint of Eqn. 2 after the application ofregularization. This could include, for example, a signal such as thefiltered IP signal shown in FIG. 3C. As shown in FIG. 4B, the resultingfrequency decomposition has a nearly constant frequency pattern alongthe time axis. The white band around f=0.25 Hz corresponds to therespiration component of the IP signal, which is the primary componentof the IP signal. The gray band around f=1.3 Hz, however, corresponds toheart rate component that is the secondary component of the IP signaland corresponds to the higher frequency ripple as shown in FIG. 3C.

To satisfy the minimized constraint of Eqn. 2 subject to Eqns. 3-5,modeling module 117 may include one or more instructions to cause CPU104 and/or GPU 106 to recursively solve Eqn. 6 as indicated by the ARXmodel. However, to further satisfy the minimized constraint of Eqn. 7subject to Eqns. 3-5, regularization module 119 may include one or moreinstructions to cause CPU 104 and/or GPU 106 to calculate and/orevaluate the gradients of the objective function (Eqn. 7) and theconstraints (Eqns. 3-5) at one or more sampled times within a processingwindow. Regularization module 119 may include instructions to facilitateany suitable technique being performed by CPU 104 and/or GPU 106 todetermine these calculations. In an embodiment, regularization module119 may include instructions that facilitate CPU 104 and/or GPU 106executing one or more of the mathematical steps described in ProvisionalPatent Application No. 61/912,616 at pages 4-5, the disclosure of whichis incorporated herein by reference in its entirety.

Adaptive Versus Non-Adaptive Embodiments

Some of the embodiments described herein discuss the calculation offilter coefficients through the use of ARX modeling of the blunt noise.That is, CPU 104 and/or GPU 106 may execute instructions stored inmodeling module 117 to calculate sets of filter coefficients that, whenapplied to an input signal, result in filtered output signals thatsatisfy the minimized constraint of Eqn. 2 through the use of an ARXmodel, such as the ARX model represented in FIG. 6, for example. Again,use of the ARX model may facilitate the calculation of blunt noisemodels having generic shapes.

ARX models also advantageously allow modeling of the blunt noise throughan analysis of past and current sampled values of the modeling data(e.g., movement parameter values) as part of a recursive calculationprocess, which is illustrated mathematically by Eqn. 6. As a result, ARXmodeling may require a large number of calculations and/or processingresources, which may be somewhat time-consuming.

Therefore, although ARX modeling embodiments may be used for bothreal-time and post-processing embodiments, ARX modeling implementationsmay be better suited to implementations of system 100 in which a signalis sampled, stored, and the filtering subsequently performed.Furthermore, the processing resources used for ARX modeling may limitits application to real-time filtering, and therefore ARX modelingembodiments may be better suited for non-adaptive filtering embodiments.Non-adaptive filtering embodiments do not change the filter parameterssuch as the Epsilon value, for example, as the signal is received inreal-time. When ARX modeling embodiments are used as part of apost-process filtering, however, adapting the filter to the signal insuch a way is less of a concern.

However, for embodiments implementing adaptive filtering techniques,less processor-intensive modeling techniques may be utilized. Forexample, signals may be filtered according to a series of successivelyreceived sliding-time windows. Within each sliding-time windows, theblunt noise may be modeled using sampled values of the modeling datawithin each sliding-time window (e.g., movement parameter values). Suchmodeling techniques may be more suitable to filtering signals inreal-time, i.e., by processing each sliding-time window as it isreceived.

Furthermore, adaptive filtering techniques may facilitate the adjustmentof filter parameters for each signal as it is received in successivesliding-time windows, thereby adapting to the signal as it is received.For example, new Epsilon values may be changed based on whether thereceived signal amplitude increases or decreases between successivesliding-time windows. In addition, other filtering processes may beperformed on a sliding-time window basis, such as the computation ofS-Transforms, for example. Such adaptive filtering may provideadditional advantages, for example, such as using more accurate Epsilonvalues that may be updated when the received signal is uncontaminatedwith blunt noise.

FIG. 5 illustrates an example method 500 in accordance with an exemplaryaspect of the present disclosure. In an embodiment, method 500 may beimplemented by any suitable computing device, such as data acquisitionsystem 102, for example, as shown in FIG. 1. In an embodiment, method500 may be performed by one or more processors executing one or morealgorithms, applications, programs, and/or routines, such as anysuitable portion of CPU 104 and/or GPU 106 executing instructions storedin one or more of data acquisition module 115, modeling module 117,regularization module 119, and/or filtering module 121, for example, asshown in FIG. 1.

Method 500 may start when one or more processors receive a signal over aprocessing window (block 502). This signal may be received, for example,via communication unit 110 of diagnostic data acquisition unit 150, asshown in FIG. 1 (block 502). In an embodiment, the signal may include aprimary signal component and blunt noise. The primary signal componentmay have an amplitude that varies over time within a maximum and aminimum amplitude. The signal may correspond to any suitable type ofsignal that may be prone to blunt noise contamination, such as an IPsignal, a periodic diagnostic medical signal having a primary component,etc. In the case of an IP signal, this primary component may correspondto the respiratory component of the IP signal.

In some embodiments, the processing window may be any suitable timeframeover which the signal is received (block 502). In such embodiments, thesignal may be sampled over the processing window for the subsequentcalculation of filter coefficients and filtering of the blunt noise fromthe signal (block 502). Such embodiments may be particularly useful forbatch processing and/or non-adaptive filtering implementations, sincelarger time intervals may be more efficiently filtered after the signalare received, sampled, and/or processed.

In other embodiments, the processing window may be any suitable slidingtimeframe (block 502). In such embodiments, the signal may be sampledover each of the successive sliding windows while filter coefficientsare calculated and filtering is performed for each successive slidingwindow. These embodiments may be particularly useful for real-timeand/or adaptive filtering implementations, since the filtering ofsignals within smaller sliding time windows may be performed inreal-time.

Method 500 may include one or more processors receiving a plurality ofmovement parameter value samples over the processing window indicativeof a source of the blunt noise (block 504). The movement parameter valuesamples may be received, for example, via communication unit 1010 ofmodeling data acquisition unit 170, as shown in FIG. 1 (block 504). Themovement parameter value samples may represent, for example,accelerometer data indicative of a patient's movement causing the bluntnoise to be introduced into the received signal (block 502).

Method 500 may include one or more processors generating a plurality ofblunt noise models to estimate the blunt noise (block 506). In anembodiment, the blunt noise models may be generated by the one or moreprocessors by applying, for each blunt noise model from among theplurality of blunt noise models, a corresponding set of filtercoefficients to the plurality of movement parameter value samples (block506). In an embodiment, the blunt noise models may be calculated usingany suitable modeling technique, such as an ARX model or a movingaverage model, for example (block 506). As previously discussed above,ARX modeling may be particularly well-suited to non-adaptive filteringembodiments, while moving average models may be better suited toadaptive, real-time filtering embodiments.

Method 500 may include one or more processors generating a plurality offiltered signals based upon a difference between the received signal(block 502) and each generated blunt noise model (block 506) from amongthe plurality of blunt noise models (block 508).

To further narrow the number of calculated filter coefficients generatedby method 500, however, method 500 may continue (block 510) to determinewhich of the calculated filter coefficients result in filtered signalshaving an amplitude less than the amplitude of the original, unfilteredsignal (block 510). In an embodiment, this may include the minimizedconstraint of solution of eqn. 2 subject to Eqns. 3-5 (block 510). Thus,as part of the filter coefficient calculation process, only those filtercoefficients that result in filtered signals satisfying the Epsilonconstraint may be retained as part of a possible set of filtercoefficient solutions (block 508), while those that do not satisfy theEpsilon constraint may be discarded or otherwise not used as part of anoptimal filter coefficient solution. An example of one of these filteredsignals that satisfies the Epsilon constraint is shown in FIG. 3B.

Method 500 may include one or more processors applying the selected setof filter coefficients having a frequency composition that is the leastfrequency-varying of the plurality of filtered signals (block 508) thatsatisfy the Epsilon constraint (block 510). In an embodiment, this mayinclude, for example, regularization in accordance with a mathematicalsolution to the minimized constraint of Eqn. 7 subject to Eqns. 3-5(block 510). In an embodiment, this regularization may be performedusing any suitable type of frequency transform algorithm, such as theS-Transform, for example. An example of an application of the selectedset of filter coefficients to a signal that satisfy the Epsilonconstraint (block 508) and provide a filtered signal that is the leastfrequency-varying of the filtered signals (block 510) is shown in FIG.3C.

As shown in FIG. 3C, for example, upon filtering the signal using theselected set of filter coefficients, the filtered signal may retain theprimary signal component while removing the blunt noise (block 510). Invarious embodiments, method 500 may perform one or more of the filtercoefficient calculation and/or selection processes in any order suitablefor the calculation of the optimal filter coefficient solution. Forexample, the processes represented in one or more of blocks 506, 508,and/or 510 may be performed concurrently or in a particular sequencewith respect to one another.

Embodiments of the present disclosure relate to one or more of thefollowing clauses.

In a first embodiment, a computer-implemented method is performed by oneor more processors to filter a signal and includes (1) receiving, by oneor more processors, a signal over a processing window, the signalincluding a primary signal component and blunt noise, the primary signalcomponent having an amplitude that varies between a maximum and minimumamplitude; (2) receiving, by one or more processors, a plurality ofmovement parameter value samples over the processing window, theplurality of movement parameter value samples being indicative of asource of the blunt noise; (3) generating, by one or more processors, aplurality of blunt noise models to estimate the blunt noise by applyinga corresponding set of filter coefficients to the plurality of movementparameter value samples; and (4) generating, by one or more processors,a plurality of filtered signals based upon a difference between thesignal and each respective blunt noise model from among the plurality ofblunt noise models by (i) selecting sets of filter coefficientscorresponding to ones of the plurality of blunt noise models thatgenerate corresponding filtered signals having amplitudes that varybetween the maximum and minimum amplitude; and (ii) filtering the signalby applying one of the sets of filter coefficients corresponding to ablunt noise model from among the plurality of blunt noise models that,when used to generate a corresponding filtered signal from among theplurality of filtered signals, has a frequency composition that is theleast frequency-varying of the plurality of filtered signals within theprocessing window to retain the primary signal component while removingthe blunt noise.

Variations of the first and other embodiments include the signalcorresponding to an impedance plethysmography (IP) signal, the primarysignal component corresponds to a respiratory component of the IPsignal, the blunt noise corresponds to an artifact introduced into theIP signal due to a person's movement, and the blunt noise having a peakamplitude that is greater than the maximum amplitude.

Variations of the first and other embodiments additionally include theact of generating the plurality of filtered signals including minimizinga constrained optimization equation:

Σ_(t=0) ^(N−1)ζ_(t)+Σ_(t=0) ^(N−1)ζ_(t) ′−cR(g,U,w), wherein:

N is the length of the processing window, ζ_(t) and ζ_(t)′ are slackvariables, c is a design parameter, g is a vector that containscontaminated signal values within the processing window, U is a matrixwhose rows are the input signals values, w is a vector of filtercoefficients, and R (g, U, w) is a regularity term that is maximizedwhen a set of filter coefficients result in a filtered signal with theleast frequency-varying spectrum, and

the constrained optimization equation is subject to:

g _(t) −y _(t)(U,w)≦ε+ζ_(t) ,t=0, . . . ,N−1,

y _(t)(U,w)−g _(t)≦ε+ζ′_(t) ,t=0, . . . ,N−1,

ζ_(t)≧0,ζ′_(t)≧0,t=0, . . . ,N−1,

wherein g_(t) represents a value of the signal at a sampling time twithin the processing window, and

wherein y_(t) (U, w) represents one of the plurality of blunt noisemodels.

Variations of the first and other embodiments further include themovement parameter value samples corresponding to accelerometer valuesin the x, y, and z-axes, and U representing a matrix having a number ofcolumns corresponding to each of the plurality of samples over theprocessing window and a number of rows corresponding to each of theaccelerometer values in the x, y, and z-axes.

Variations of the first and other embodiments also include generatingthe plurality of blunt noise models by generating an autoregressiveexogenous model according to the equation:

y _(t)=Σ_(i=1) ^(n) ^(a) a _(i) y _(t−i)+Σ_(i=1) ^(n) ^(b) u_(t−i+1),wherein:

y_(t) is equal to a value of one of the plurality of filtered signals ata sampling time t within the processing window, n_(a) is equal to anumber of filter poles, n_(b) is equal to a number of filter zeroes plusone, a_(i) is a i-th feedback coefficient from among the correspondingset of filter coefficients, b_(i) is a i-th feedforward coefficient setfrom among the corresponding set of filter coefficients, u_(t) is avector including the x, y, and z-axis accelerometer values at a samplingtime t within the processing window, and wherein w represents a vectorthat minimizes the constrained optimization equation and includesfeedback coefficients and feedforward coefficients from among thecorresponding set of filter coefficients.

Variations of the first and other embodiments also include selecting oneof the sets of filter coefficients by (1) calculating a Stockwelltransform of each of the plurality of filtered signals to generate aplurality of respective filtered signal frequency decompositions; (2)calculating, for each of the filtered signal frequency decompositions,an average correlation between frequency components over a plurality ofsamples within the processing window; and (3) determining, by one ormore processors, which of the plurality of filtered signals has afrequency composition that is the least frequency-varying based upon theaverage correlation of between frequency components for each of thefiltered signal frequency decompositions.

Variations of the first and other embodiments also include the signalbeing filtered in real-time as the signal is received and/or the signalbeing filtered as part of a batch processing after the signal isreceived.

Variations of the first and other embodiments also include the signalincluding one or more of an electrocardiogram, an impedance cardiograph,an impedance-based blood volume waveform, an arterial blood pressurewaveform, a venous blood pressure waveform, an intracranial pressurewaveform, a photoplethysmography waveform, an end-tidal carbon dioxidewaveform, a Doppler signal, and/or a piezoelectric signal.

In a second embodiment, a data acquisition system is disclosed that isconfigured to filter a signal by (1) receiving the signal over aprocessing window, the signal including a primary signal component andblunt noise, the primary signal component having an amplitude thatvaries between a maximum and minimum amplitude; (2) receiving aplurality of movement parameter value samples over the processingwindow, the plurality of movement parameter value samples beingindicative of a source of the blunt noise; (3) generating a plurality ofblunt noise models to estimate the blunt noise by applying acorresponding set of filter coefficients to the plurality of movementparameter value samples; and (4) generating a plurality of filteredsignals based upon a difference between the signal and each respectiveblunt noise model from among the plurality of blunt noise models by (i)selecting sets of filter coefficients corresponding to ones of theplurality of blunt noise models that generate corresponding filteredsignals having amplitudes that vary between the maximum and minimumamplitude; and (ii) filtering the signal by applying one of the sets offilter coefficients corresponding to a blunt noise model from among theplurality of blunt noise models that, when used to generate acorresponding filtered signal from among the plurality of filteredsignals, has a frequency composition that is the least frequency-varyingof the plurality of filtered signals within the processing window toretain the primary signal component while removing the blunt noise.

Variations of the second and other embodiments include the signalcorresponding to an impedance plethysmography (IP) signal, the primarysignal component corresponds to a respiratory component of the IPsignal, the blunt noise corresponds to an artifact introduced into theIP signal due to a person's movement, and the blunt noise having a peakamplitude that is greater than the maximum amplitude.

Variations of the second and other embodiments additionally include thedata acquisition system generating the plurality of filtered signalsincluding minimizing a constrained optimization equation:

Σ_(t=0) ^(N−1)ζ_(t)+Σ_(t=0) ^(N−1)ζ_(t) ′−cR(g,U,w), wherein:

N is the length of the processing window, ζ_(t) and ζ_(t)′ are slackvariables, c is a design parameter, g is a vector that containscontaminated signal values within the processing window, U is a matrixwhose rows are the input signals values, w is a vector of filtercoefficients, and R (g, U, w) is a regularity term that is maximizedwhen a set of filter coefficients result in a filtered signal with theleast frequency-varying spectrum, and

the constrained optimization equation is subject to:

g _(t) −y _(t)(U,w)≦ε+ζ_(t) ,t=0, . . . ,N−1,

y _(t)(U,w)−g _(t)≦ε+ζ′_(t) ,t=0, . . . ,N−1,

ζ_(t)≧0,ζ′_(t)≧0,t=0, . . . ,N−1,

wherein g_(t) represents a value of the signal at a sampling time twithin the processing window, and

wherein y_(t) (U, w) represents one of the plurality of blunt noisemodels.

Variations of the second and other embodiments further include themovement parameter value samples corresponding to accelerometer valuesin the x, y, and z-axes, and U representing a matrix having a number ofcolumns corresponding to each of the plurality of samples over theprocessing window and a number of rows corresponding to each of theaccelerometer values in the x, y, and z-axes.

Variations of the second and other embodiments also include the dataacquisition system generating the plurality of blunt noise models bygenerating an autoregressive exogenous model according to the equation:

y _(t)=−Σ_(i=1) ^(n) ^(a) a _(i) y _(t−1)+Σ_(i=1) ^(n) ^(b) b _(i) ^(T)u _(t−i+1), wherein:

y_(t) is equal to a value of one of the plurality of filtered signals ata sampling time t within the processing window, n_(a) is equal to anumber of filter poles, n_(b) is equal to a number of filter zeroes plusone, a_(i) is a i-th feedback coefficient from among the correspondingset of filter coefficients, b_(i) is a i-th feedforward coefficient setfrom among the corresponding set of filter coefficients, u_(t) is avector including the x, y, and z-axis accelerometer values at a samplingtime t within the processing window, and wherein w represents a vectorthat minimizes the constrained optimization equation and includesfeedback coefficients and feedforward coefficients from among thecorresponding set of filter coefficients.

Variations of the second and other embodiments also include the dataacquisition system selecting one of the sets of filter coefficients by(1) calculating a Stockwell transform of each of the plurality offiltered signals to generate a plurality of respective filtered signalfrequency decompositions; (2) calculating, for each of the filteredsignal frequency decompositions, an average correlation betweenfrequency components over a plurality of samples within the processingwindow; and (3) determining, by one or more processors, which of theplurality of filtered signals has a frequency composition that is theleast frequency-varying based upon the average correlation of betweenfrequency components for each of the filtered signal frequencydecompositions.

Variations of the second and other embodiments also include the dataacquisition system filtering the signal in real-time as the signal isreceived and/or filtering the signal as part of a batch processing afterthe signal is received.

Variations of the second and other embodiments also include the signalincluding one or more of an electrocardiogram, an impedance cardiograph,an impedance-based blood volume waveform, an arterial blood pressurewaveform, a venous blood pressure waveform, an intracranial pressurewaveform, a photoplethysmography waveform, an end-tidal carbon dioxidewaveform, a Doppler signal, and/or a piezoelectric signal.

In a third embodiment, a non-transitory computer readable media havinginstructions stored thereon in a data acquisition device is executed bya processor to cause the processor to (1) receive a signal over aprocessing window, the signal including a primary signal component andblunt noise, the primary signal component having an amplitude thatvaries between a maximum and minimum amplitude; (2) receive a pluralityof movement parameter value samples over the processing window, theplurality of movement parameter value samples being indicative of asource of the blunt noise; (3) generate a plurality of blunt noisemodels to estimate the blunt noise by applying a corresponding set offilter coefficients to the plurality of movement parameter valuesamples; and (4) generate a plurality of filtered signals based upon adifference between the signal and each respective blunt noise model fromamong the plurality of blunt noise models by (i) selecting sets offilter coefficients corresponding to ones of the plurality of bluntnoise models that generate corresponding filtered signals havingamplitudes that vary between the maximum and minimum amplitude; and (ii)filtering the signal by applying one of the sets of filter coefficientscorresponding to a blunt noise model from among the plurality of bluntnoise models that, when used to generate a corresponding filtered signalfrom among the plurality of filtered signals, has a frequencycomposition that is the least frequency-varying of the plurality offiltered signals within the processing window to retain the primarysignal component while removing the blunt noise.

Variations of the third and other embodiments include the signalcorresponding to an impedance plethysmography (IP) signal, the primarysignal component corresponds to a respiratory component of the IPsignal, the blunt noise corresponds to an artifact introduced into theIP signal due to a person's movement, and the blunt noise having a peakamplitude that is greater than the maximum amplitude.

Variations of the third and other embodiments additionally theinstructions being executed by a processor to cause the processor togenerate the plurality of filtered signals including minimizing aconstrained optimization equation:

Σ_(t=0) ^(N−1)ζ_(t)+Σ_(t=0) ^(N−1)ζ_(t) ′−cR(g,U,w), wherein:

N is the length of the processing window, ζ_(t) and ζ_(t)′ are slackvariables, c is a design parameter, g is a vector that containscontaminated signal values within the processing window, U is a matrixwhose rows are the input signals values, w is a vector of filtercoefficients, and R (g, U, w) is a regularity term that is maximizedwhen a set of filter coefficients result in a filtered signal with theleast frequency-varying spectrum, and

the constrained optimization equation is subject to:

g _(t) −y _(t)(U,w)≦ε+ζ_(t) ,t=0, . . . ,N−1,

y _(t)(U,w)−g _(t)≦εζ′_(t) ,t=0, . . . ,N−1,

ζ_(t)≧0,ζ′_(t)≧0,t=0, . . . ,N−1,

wherein g_(t) represents a value of the signal at a sampling time twithin the processing window, and

wherein y_(t) (U, w) represents one of the plurality of blunt noisemodels.

Variations of the third and other embodiments further include themovement parameter value samples corresponding to accelerometer valuesin the x, y, and z-axes, and U representing a matrix having a number ofcolumns corresponding to each of the plurality of samples over theprocessing window and a number of rows corresponding to each of theaccelerometer values in the x, y, and z-axes.

Variations of the third and other embodiments also include theinstructions being executed by a processor to cause the processor togenerate the plurality of blunt noise models by generating anautoregressive exogenous model according to the equation:

y _(t)=−Σ_(i=1) ^(n) ^(a) a _(i) y _(t−1)+Σ_(i=1) ^(n) ^(b) b _(i) ^(T)u _(t−i+1), wherein:

y_(t) is equal to a value of one of the plurality of filtered signals ata sampling time t within the processing window, n_(a) is equal to anumber of filter poles, n_(b) is equal to a number of filter zeroes plusone, a_(i) is a i-th feedback coefficient from among the correspondingset of filter coefficients, b_(i) is a i-th feedforward coefficient setfrom among the corresponding set of filter coefficients, u_(t) is avector including the x, y, and z-axis accelerometer values at a samplingtime t within the processing window, and wherein w represents a vectorthat minimizes the constrained optimization equation and includesfeedback coefficients and feedforward coefficients from among thecorresponding set of filter coefficients.

Variations of the third and other embodiments also include theinstructions being executed by a processor to cause the processor toselect one of the sets of filter coefficients by (1) calculating aStockwell transform of each of the plurality of filtered signals togenerate a plurality of respective filtered signal frequencydecompositions; (2) calculating, for each of the filtered signalfrequency decompositions, an average correlation between frequencycomponents over a plurality of samples within the processing window; and(3) determining, by one or more processors, which of the plurality offiltered signals has a frequency composition that is the leastfrequency-varying based upon the average correlation of betweenfrequency components for each of the filtered signal frequencydecompositions.

Variations of the third and other embodiments also include theinstructions being executed by a processor to cause the processor tofilter the signal in real-time as the signal is received and/or tofilter the signal as part of a batch processing after the signal isreceived.

Variations of the third and other embodiments also include the signalincluding one or more of an electrocardiogram, an impedance cardiograph,an impedance-based blood volume waveform, an arterial blood pressurewaveform, a venous blood pressure waveform, an intracranial pressurewaveform, a photoplethysmography waveform, an end-tidal carbon dioxidewaveform, a Doppler signal, and/or a piezoelectric signal.

Throughout this specification, plural instances may implementcomponents, operations, or structures described as a single instance.Although individual operations of one or more methods are illustratedand described as separate operations, one or more of the individualoperations may be performed concurrently, and nothing requires that theoperations be performed in the order illustrated. Structures andfunctionality presented as separate components in example configurationsmay be implemented as a combined structure or component.

Similarly, structures and functionality presented as a single componentmay be implemented as separate components. These and other variations,modifications, additions, and improvements fall within the scope of thesubject matter herein.

Additionally, certain embodiments are described herein as includinglogic or a number of routines, subroutines, applications, orinstructions. These may constitute either software (e.g., code embodiedon a machine-readable medium or in a transmission signal) or hardware.In hardware, the routines, etc., are tangible units capable ofperforming certain operations and may be configured or arranged in acertain manner. In example embodiments, one or more computer systems(e.g., a standalone, client or server computer system) or one or morehardware modules of a computer system (e.g., a processor or a group ofprocessors) may be configured by software (e.g., an application orapplication portion) as a hardware module that operates to performcertain operations as described herein.

In various embodiments, a hardware module may be implementedmechanically or electronically. For example, a hardware module maycomprise dedicated circuitry or logic that is permanently configured(e.g., as a special-purpose processor, such as a field programmable gatearray (FPGA) or an application-specific integrated circuit (ASIC)) toperform certain operations. A hardware module may also compriseprogrammable logic or circuitry (e.g., as encompassed within ageneral-purpose processor or other programmable processor) that istemporarily configured by software to perform certain operations. Itwill be appreciated that the decision to implement a hardware modulemechanically, in dedicated and permanently configured circuitry, or intemporarily configured circuitry (e.g., configured by software) may bedriven by cost and time considerations.

Accordingly, the term “hardware module” should be understood toencompass a tangible entity, be that an entity that is physicallyconstructed, permanently configured (e.g., hardwired), or temporarilyconfigured (e.g., programmed) to operate in a certain manner or toperform certain operations described herein. Considering embodiments inwhich hardware modules are temporarily configured (e.g., programmed),each of the hardware modules need not be configured or instantiated atany one instance in time. For example, where the hardware modulescomprise a general-purpose processor configured using software, thegeneral-purpose processor may be configured as respective differenthardware modules at different times. Software may accordingly configurea processor, for example, to constitute a particular hardware module atone instance of time and to constitute a different hardware module at adifferent instance of time.

Hardware modules can provide information to, and receive informationfrom, other hardware modules. Accordingly, the described hardwaremodules may be regarded as being communicatively coupled. Where multipleof such hardware modules exist contemporaneously, communications may beachieved through signal transmission (e.g., over appropriate circuitsand buses) that connects the hardware modules. In embodiments in whichmultiple hardware modules are configured or instantiated at differenttimes, communications between such hardware modules may be achieved, forexample, through the storage and retrieval of information in memorystructures to which the multiple hardware modules have access. Forexample, one hardware module may perform an operation and store theoutput of that operation in a memory device to which it iscommunicatively coupled. A further hardware module may then, at a latertime, access the memory device to retrieve and process the storedoutput. Hardware modules may also initiate communications with input oroutput devices, and can operate on a resource (e.g., a collection ofinformation).

The various operations of the example methods described herein may beperformed, at least partially, by one or more processors that aretemporarily configured (e.g., by software) or permanently configured toperform the relevant operations. Whether temporarily or permanentlyconfigured, such processors may constitute processor-implemented modulesthat operate to perform one or more operations or functions. The modulesreferred to herein may, in some example embodiments, compriseprocessor-implemented modules.

Similarly, the methods or routines described herein may be at leastpartially processor-implemented. For example, at least some of theoperations of a method may be performed by one or more processors orprocessor-implemented hardware modules. The performance of certain ofthe operations may be distributed among the one or more processors, notonly residing within a single machine, but also deployed across a numberof machines. In some example embodiments, the processor or processorsmay be located in a single location (e.g., within a home environment, anoffice environment or as a server farm), while in other embodiments theprocessors may be distributed across a number of locations.

The performance of certain of the operations may be distributed amongthe one or more processors, not only residing within a single machine,but also deployed across a number of machines. In some exampleembodiments, the one or more processors or processor-implemented modulesmay be located in a single geographic location (e.g., within a homeenvironment, an office environment, or a server farm). In other exampleembodiments, the one or more processors or processor-implemented modulesmay be distributed across a number of geographic locations.

Unless specifically stated otherwise, discussions herein using wordssuch as “processing,” “computing,” “calculating,” “determining,”“presenting,” “displaying,” or the like may refer to actions orprocesses of a machine (e.g., a computer) that manipulates or transformsdata represented as physical (e.g., electronic, magnetic, or optical)quantities within one or more memories (e.g., volatile memory,non-volatile memory, or a combination thereof), registers, or othermachine components that receive, store, transmit, or displayinformation.

As used herein any reference to “one embodiment” or “an embodiment”means that a particular element, feature, structure, or characteristicdescribed in connection with the embodiment is included in at least oneembodiment. The appearances of the phrase “in one embodiment” in variousplaces in the specification are not necessarily all referring to thesame embodiment.

Some embodiments may be described using the expression “coupled” and“connected” along with their derivatives. For example, some embodimentsmay be described using the term “coupled” to indicate that two or moreelements are in direct physical or electrical contact. The term“coupled,” however, may also mean that two or more elements are not indirect contact with each other, but yet still co-operate or interactwith each other. The embodiments are not limited in this context.

As used herein, the terms “comprises,” “comprising,” “includes,”“including,” “has,” “having” or any other variation thereof, areintended to cover a non-exclusive inclusion. For example, a process,method, article, or apparatus that comprises a list of elements is notnecessarily limited to only those elements but may include otherelements not expressly listed or inherent to such process, method,article, or apparatus. Further, unless expressly stated to the contrary,“or” refers to an inclusive or and not to an exclusive or. For example,a condition A or B is satisfied by any one of the following: A is true(or present) and B is false (or not present), A is false (or notpresent) and B is true (or present), and both A and B are true (orpresent).

In addition, use of the “a” or “an” are employed to describe elementsand components of the embodiments herein. This is done merely forconvenience and to give a general sense of the description. Thisdescription, and the claims that follow, should be read to include oneor at least one and the singular also includes the plural unless it isobvious that it is meant otherwise.

This detailed description is to be construed as an example only and doesnot describe every possible embodiment, as describing every possibleembodiment would be impractical, if not impossible. One could implementnumerous alternate embodiments, using either current technology ortechnology developed after the filing date of this application.

What is claimed:
 1. A computer-implemented method of filtering a signal,comprising: receiving, by one or more processors, a signal over aprocessing window, the signal including a primary signal component andblunt noise, the primary signal component having an amplitude thatvaries between a maximum and minimum amplitude; receiving, by one ormore processors, a plurality of movement parameter value samples overthe processing window, the plurality of movement parameter value samplesbeing indicative of a source of the blunt noise; generating, by one ormore processors, a plurality of blunt noise models to estimate the bluntnoise by applying a corresponding set of filter coefficients to theplurality of movement parameter value samples to generate each bluntnoise model from among the plurality of blunt noise models; generating,by one or more processors, a plurality of filtered signals based upon adifference between the signal and each respective blunt noise model fromamong the plurality of blunt noise models by: (i) selecting sets offilter coefficients corresponding to ones of the plurality of bluntnoise models that generate corresponding filtered signals havingamplitudes that vary between the maximum and minimum amplitude; and (ii)filtering the signal by applying one of the sets of filter coefficientscorresponding to a blunt noise model from among the plurality of bluntnoise models that, when used to generate a corresponding filtered signalfrom among the plurality of filtered signals, has a frequencycomposition that is the least frequency-varying of the plurality offiltered signals within the processing window to retain the primarysignal component while removing the blunt noise.
 2. Thecomputer-implemented method of claim 1, wherein: the signal correspondsto an impedance plethysmography (IP) signal, the primary signalcomponent corresponds to a respiratory component of the IP signal, theblunt noise corresponds to an artifact introduced into the IP signal dueto a person's movement, and the blunt noise having a peak amplitude thatis greater than the maximum amplitude.
 3. The computer-implementedmethod of claim 1, wherein the act of generating the plurality offiltered signals comprises: minimizing a constrained optimizationequation:Σ_(t=0) ^(N−1)ζ_(t)+Σ_(t=0) ^(N−1)ζ_(t) ′−cR(g,U,w), wherein: N is thelength of the processing window, ζ_(t) and ζ_(t)′ are slack variables, cis a design parameter, g is a vector that contains contaminated signalvalues within the processing window, U is a matrix whose rows are theinput signals values, w is a vector of filter coefficients, and R (g, U,w) is a regularity term that is maximized when a set of filtercoefficients result in a filtered signal with the leastfrequency-varying spectrum, and the constrained optimization equation issubject to:g _(t) −t _(t)(U,w)≦ε+ζ_(t) ,t=0, . . . ,N−1,  (3)y _(t)(U,w)−g _(t)≦ε+ζ′_(t) ,t=0, . . . ,N−1,  (4)ζ_(t)≧0,ζ_(t)′≧0,t=0, . . . ,N−1,  (5) wherein g_(t) represents a valueof the signal at a sampling time t within the processing window, andwherein y_(t) (U, w) represents one of the plurality of blunt noisemodels.
 4. The computer-implemented method of claim 3, wherein: themovement parameter value samples correspond to accelerometer values inthe x, y, and z-axes, and U represents a matrix having a number ofcolumns corresponding to each of the plurality of samples over theprocessing window and a number of rows corresponding to each of theaccelerometer values in the x, y, and z-axes.
 5. Thecomputer-implemented method of claim 4, and wherein the act ofgenerating the plurality of blunt noise models comprises: generating anautoregressive exogenous model according to the equation:y _(t)=−Σ_(i=1) ^(n) ^(a) a _(i) y _(t−1)+Σ_(i=1) ^(n) ^(b) b _(i) ^(T)u _(t−i+1), wherein: y_(t) is equal to a value of one of the pluralityof filtered signals at a sampling time t within the processing window,n_(a) is equal to a number of filter poles, n_(b) is equal to a numberof filter zeroes plus one, a_(i) is a i-th feedback coefficient fromamong the corresponding set of filter coefficients, b_(i) is a i-thfeedforward coefficient set from among the corresponding set of filtercoefficients, u_(t) is a vector including the x, y, and z-axisaccelerometer values at a sampling time t within the processing window,and wherein w represents a vector that minimizes the constrainedoptimization equation and includes feedback coefficients and feedforwardcoefficients from among the corresponding set of filter coefficients. 6.The computer-implemented method of claim 1, wherein the act of selectingone of the sets of filter coefficients comprises: calculating aStockwell transform of each of the plurality of filtered signals togenerate a plurality of respective filtered signal frequencydecompositions; calculating, for each of the filtered signal frequencydecompositions, an average correlation between frequency components overa plurality of samples within the processing window; and determining, byone or more processors, which of the plurality of filtered signals has afrequency composition that is the least frequency-varying based upon theaverage correlation of between frequency components for each of thefiltered signal frequency decompositions.
 7. The computer-implementedmethod of claim 1, wherein the signal is filtered in real-time as thesignal is received.
 8. The computer-implemented method of claim 1,wherein the signal is filtered as part of a batch processing after thesignal is received.
 9. The computer-implemented method of claim 1,wherein the signal includes one or more of the following: anelectrocardiogram; an impedance cardiograph; an impedance-based bloodvolume waveform; an arterial blood pressure waveform; a venous bloodpressure waveform; an intracranial pressure waveform; aphotoplethysmography waveform; an end-tidal carbon dioxide waveform; aDoppler signal; and a piezoelectric signal.
 10. A data acquisitionsystem to filter a signal, comprising: a communication unit configuredto: receive a signal over a processing window, the signal including aprimary signal component and blunt noise, the primary signal componenthaving an amplitude that varies between a maximum and minimum amplitude;receive a plurality of movement parameter value samples over theprocessing window, the plurality of movement parameter value samplesbeing indicative of a source of the blunt noise; and a centralprocessing unit (CPU) configured to: generate a plurality of blunt noisemodels to estimate the blunt noise by applying a corresponding set offilter coefficients to the plurality of movement parameter valuesamples; generate a plurality of filtered signals based upon adifference between the signal and each respective blunt noise model fromamong the plurality of blunt noise models by: (i) selecting sets offilter coefficients corresponding to ones of the plurality of bluntnoise models that generate corresponding filtered signals havingamplitudes that vary between the maximum and minimum amplitude; and (ii)filtering the signal by applying one of the sets of filter coefficientscorresponding to a blunt noise model from among the plurality of bluntnoise models that, when used to generate a corresponding filtered signalfrom among the plurality of filtered signals, has a frequencycomposition that is the least frequency-varying of the plurality offiltered signals within the processing window to retain the primarysignal component while removing the blunt noise.
 11. The dataacquisition system of claim 10, wherein: the signal corresponds to animpedance plethysmography (IP) signal, the primary signal componentcorresponds to a respiratory component of the IP signal, the blunt noisecorresponds to an artifact introduced into the IP signal due to aperson's movement, and the blunt noise having a peak amplitude that isgreater than the maximum amplitude.
 12. The data acquisition system ofclaim 10, wherein the CPU is further configured to generate theplurality of filtered signals by: minimizing a constrained optimizationequation:Σ_(t=0) ^(N−1)ζ_(t)+Σ_(t=0) ^(N−1)ζ_(t) ′−cR(g,U,w), wherein: N is thelength of the processing window, ζ_(t) and ζ_(t)′ are slack variables, cis a design parameter, g is a vector that contains contaminated signalvalues within the processing window, U is a matrix whose rows are theinput signals values, w is a vector of filter coefficients, and R (g, U,w) is a regularity term that is maximized when a set of filtercoefficients result in a filtered signal with the leastfrequency-varying spectrum, and the constrained optimization equation issubject to:g _(t) −t _(t)(U,w)≦ε+ζ_(t) ,t=0, . . . ,N−1,  (3)y _(t)(U,w)−g _(t)≦ε+ζ′_(t) ,t=0, . . . ,N−1,  (4)ζ_(t)≧0,ζ_(t)′≧0,t=0, . . . ,N−1,  (5) wherein g_(t) represents a valueof the signal at a sampling time t within the processing window, andwherein y_(t) (U, w) represents one of the plurality of blunt noisemodels.
 13. The data acquisition system of claim 12, wherein: themovement parameter value samples correspond to accelerometer values inthe x, y, and z-axes, and U represents a matrix having a number ofcolumns corresponding to each of the plurality of samples over theprocessing window and a number of rows corresponding to each of theaccelerometer values in the x, y, and z-axes.
 14. The data acquisitionsystem of claim 13, wherein the CPU is further configured to generatethe plurality of blunt noise models by: generating an autoregressiveexogenous model according to the equation:y _(t)=−Σ_(i=1) ^(n) ^(a) a _(i) y _(t−1)+Σ_(i=1) ^(n) ^(b) b _(i) ^(T)u _(t−i+1), wherein: y_(t) is equal to a value of one of the pluralityof filtered signals at a sampling time t within the processing window,n_(a) is equal to a number of filter poles, n_(b) is equal to a numberof filter zeroes plus one, a_(i) is a i-th feedback coefficient fromamong the corresponding set of filter coefficients, b_(i) is a i-thfeedforward coefficient set from among the corresponding set of filtercoefficients, u_(t) is a vector including the x, y, and z-axisaccelerometer values at a sampling time t within the processing window,and wherein w represents a vector that minimizes the constrainedoptimization equation and includes feedback coefficients and feedforwardcoefficients from among the corresponding set of filter coefficients.15. The data acquisition system of claim 10, wherein the CPU is furtherconfigured to select one of the sets of filter coefficients by:calculating a Stockwell transform of each of the plurality of filteredsignals to generate a plurality of respective filtered signal frequencydecompositions; calculating, for each of the filtered signal frequencydecompositions, an average correlation between frequency components overa plurality of samples within the processing window; and determiningwhich of the plurality of filtered signals has a frequency compositionthat is the least frequency-varying based upon the average correlationof between frequency components for each of the filtered signalfrequency decompositions.
 16. The data acquisition system of claim 10,wherein the CPU is further configured to filter the signal in real-timeas the signal is received.
 17. The data acquisition system of claim 10,wherein the CPU is further configured to filter the signal as part of abatch process after the signal is received.
 18. The data acquisitionsystem of claim 10, wherein the signal includes one or more of thefollowing: an electrocardiogram; an impedance cardiograph; animpedance-based blood volume waveform; an arterial blood pressurewaveform; a venous blood pressure waveform; an intracranial pressurewaveform; a photoplethysmography waveform; an end-tidal carbon dioxidewaveform; a Doppler signal; and a piezoelectric signal.
 19. Anon-transitory, tangible computer-readable medium storing machinereadable instructions for filtering a signal that, when executed by aprocessor, cause the processor to: receive a signal over a processingwindow, the signal including a primary signal component and blunt noise,the primary signal component having an amplitude that varies between amaximum and minimum amplitude; receive a plurality of movement parametervalue samples over the processing window, the plurality of movementparameter value samples being indicative of a source of the blunt noise;generate a plurality of blunt noise models to estimate the blunt noiseby applying a corresponding set of filter coefficients to the pluralityof movement parameter value samples; generate a plurality of filteredsignals based upon a difference between the signal and each respectiveblunt noise model from among the plurality of blunt noise models by: (i)selecting sets of filter coefficients corresponding to ones of theplurality of blunt noise models that generate corresponding filteredsignals having amplitudes that vary between the maximum and minimumamplitude; and (ii) filtering the signal by applying one of the sets offilter coefficients corresponding to a blunt noise model from among theplurality of blunt noise models that, when used to generate acorresponding filtered signal from among the plurality of filteredsignals, has a frequency composition that is the least frequency-varyingof the plurality of filtered signals within the processing window toretain the primary signal component while removing the blunt noise. 20.The non-transitory, tangible computer-readable medium of claim 19,wherein: the signal corresponds to an impedance plethysmography (IP)signal, the primary signal component corresponds to a respiratorycomponent of the IP signal, the blunt noise corresponds to an artifactintroduced into the IP signal due to a person's movement, and the bluntnoise having a peak amplitude that is greater than the maximumamplitude.
 21. The non-transitory, tangible computer-readable medium ofclaim 19, wherein the instructions to generate the plurality of filteredsignals include instructions that cause the processor to: minimize aconstrained optimization equation:Σ_(t=0) ^(N−1)ζ_(t)+Σ_(t=0) ^(N−1)ζ_(t) ′−cR(g,U,w), wherein: N is thelength of the processing window, ζ_(t) and ζ_(t)′ are slack variables, cis a design parameter, g is a vector that contains contaminated signalvalues within the processing window, U is a matrix whose rows are theinput signals values, w is a vector of filter coefficients, and R (g, U,w) is a regularity term that is maximized when a set of filtercoefficients result in a filtered signal with the leastfrequency-varying spectrum, and the constrained optimization equation issubject to:g _(t) −t _(t)(U,w)≦ε+ζ_(t) ,t=0, . . . ,N−1,  (3)y _(t)(U,w)−g _(t)≦ε+ζ′_(t) ,t=0, . . . ,N−1,  (4)ζ_(t)≧0,ζ_(t)′≧0,t=0, . . . ,N−1,  (5) wherein g_(t) represents a valueof the signal at a sampling time t within the processing window, andwherein y_(t) (U, w) represents one of the plurality of blunt noisemodels.
 22. The non-transitory, tangible computer-readable medium ofclaim 21, wherein: the movement parameter value samples correspond toaccelerometer values in the x, y, and z-axes, and U represents a matrixhaving a number of columns corresponding to each of the plurality ofsamples over the processing window and a number of rows corresponding toeach of the accelerometer values in the x, y, and z-axes.
 23. Thenon-transitory, tangible computer-readable medium of claim 24, whereinthe instructions to generate the plurality of blunt noise models includeinstructions that cause the processor to: generate an autoregressiveexogenous model according to the equation:y _(t)=−Σ_(i=1) ^(n) ^(a) a _(i) y _(t−1)+Σ_(i=1) ^(n) ^(b) b _(i) ^(T)u _(t−i+1), wherein: y_(t) is equal to a value of one of the pluralityof filtered signals at a sampling time t within the processing window,n_(a) is equal to a number of filter poles, n_(b) is equal to a numberof filter zeroes plus one, a_(i) is a i-th feedback coefficient fromamong the corresponding set of filter coefficients, b_(i) is a i-thfeedforward coefficient set from among the corresponding set of filtercoefficients, u_(t) is a vector including the x, y, and z-axisaccelerometer values at a sampling time t within the processing window,and wherein w represents a vector that minimizes the constrainedoptimization equation and includes feedback coefficients and feedforwardcoefficients from among the corresponding set of filter coefficients.24. The non-transitory, tangible computer-readable medium of claim 19,wherein the instructions to select one of the sets of filtercoefficients include instructions that cause the processor to: calculatea Stockwell transform of each of the plurality of filtered signals togenerate a plurality of respective filtered signal frequencydecompositions; calculate, for each of the filtered signal frequencydecompositions, an average correlation between frequency components overa plurality of samples within the processing window; and determine whichof the plurality of filtered signals has a frequency composition that isthe least frequency-varying based upon the average correlation ofbetween frequency components for each of the filtered signal frequencydecompositions.
 25. The non-transitory, tangible computer-readablemedium of claim 19, wherein the signal is filtered in real-time as thesignal is received.
 26. The non-transitory, tangible computer-readablemedium of claim 19, wherein the signal is filtered as part of a batchprocessing after the signal is received.
 27. The non-transitory,tangible computer-readable medium of claim 19, wherein the signalincludes one or more of the following: an electrocardiogram; animpedance cardiograph; an impedance-based blood volume waveform; anarterial blood pressure waveform; a venous blood pressure waveform; anintracranial pressure waveform; a photoplethysmography waveform; anend-tidal carbon dioxide waveform; a Doppler signal; and a piezoelectricsignal.